{
  "abstract": "We study fully online fixed-confidence causal discovery without any historical observational data. Starting from zero samples, the learner sequentially selects interventions to recover both the causal DAG and its edge weights under a linear-Gaussian structural equation model. We establish an instance-dependent lower bound for any $(ε,δ)$-correct algorithm and propose \\textsc{FOCUS}, which adaptively allocates interventions through an online max--min game. A key contribution is a computable concentration inequality for the accumulated KL divergence involving causal parameters shared across interventions. We prove that \\textsc{FOCUS} is $(ε,δ)$-correct and that its expected stopping time matches the lower bound in its $Θ(\\log(1/δ))$ dependence up to an instance-dependent constant. Experiments demonstrate improved structure and edge-weight recovery and confirm the predicted stopping-time trend. Our codes are available on https://anonymous.4open.science/r/FOCUS_code-76E5",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32165",
  "author_total": 2,
  "authors": [
    {
      "name": "Haijie Xu"
    },
    {
      "name": "Chen Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6b447b09f0qjx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32165",
  "fulltext_url": null,
  "id": "6b447b09f0qjx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32165",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7214807905",
  "pdf_url": "https://arxiv.org/pdf/2609.32165",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6b447b09f0qjx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.32165",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32165"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "FOCUS: Fixed-Confidence Online Causal Learning Using Sequential Adaptive Interventions",
  "title_text": "FOCUS: Fixed-Confidence Online Causal Learning Using Sequential Adaptive Interventions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/6b447b09f0qjx",
  "venue": "arXiv",
  "versions": []
}